Q: What are the prime factors of the number 231,410,025?

 A: 3, 5, 7, 11, 19, 37

Why are those the prime factors of the number 231,410,025?

Prime factors are the prime numbers that can be multipled together to equal the original number. You find the factors by dividing by prime numbers. It is best shown by creating a Factor Tree.

Factor Tree for the number 231,410,025

231,410,025
Factor Arrows
377,136,675
Factor Arrows
325,712,225
Factor Arrows
55,142,445
Factor Arrows
51,028,489
Factor Arrows
7146,927
Factor Arrows
1113,357
Factor Arrows
19703
Factor Arrows
1937

The numbers in bold above are the prime factors. If there are multiples, you only count them one time. This leads us to our prime factors of:

3, 5, 7, 11, 19, 37

We can check our work by multiplying all of the prime factors together: 3 x 3 x 5 x 5 x 7 x 11 x 19 x 19 x 37 = 231,410,025

This can also be written as 32 x 52 x 71 x 111 x 192 x 371 = 231,410,025

If you would like to know more, or need additional explanation, please review our prime factorization explanation.


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